Internet of Things (IoT) applications can play a critical role in business and industry. Industrial IoT (IIoT) refers to the use of IoT technologies in manufacturing. Enabling IIoT applications in cloud environments requires the design of appropriate IIoT Platform as-a-Service (IIoT PaaS) to support and ease their provisioning (i.e., development, deployment and management). This paper critically reviews the IIoT PaaS architectures proposed so far in the relevant literature. It only surveys the architectures that are suitable for IIoT applications provisioning and it excludes regular IoT solutions from its scope. The evaluation is based on a set of well-defined architectural requirements. It also introduces and discusses the future challenges and the research directions. The critical review discusses the PaaS solutions that focus on the whole spectrum of IoT verticals and also the ones dealing with specific IoT verticals. Existing limitations are identified and hints are provided on how to tackle them. As critical research directions, the mechanisms that enable the secure provisioning, and IIoT PaaS interaction with virtualized IoT Infrastructure as-a-Service (IaaS) and fog computing layer are discussed.